# How do you factor 22x^2 + 51x - 10?

Aug 11, 2015

Factor: $y = 22 {x}^{2} + 51 x - 10$

Ans: (11x - 2)(2x + 5)

#### Explanation:

I use the new AC Method. Factored form: y = 22(x + p)(x + q).
Converted trinomial: $y ' = {x}^{2} + 51 x - 220.$ Find 2 numbers p' and q' knowing sum (-51) and product (-220). p' and q' have opposite signs.
Factor pairs of (220) --> ...(-2, 49)(-4, 55). This sum is 51 = b.
Then, p' = -4 and q' = 55.
Therefor: $p = - \frac{4}{22} = - \frac{2}{11}$ and $q = \frac{55}{22} = \frac{5}{2}$

y = 22(x - 2/11)(x + 5/2) = (11x - 2)(2x + 5)